Group #29597468 — subgroups

Subgroups — #29597468

Order 15616.

458 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21458922	C₂	1	1	yes	maximal, characteristic
2	#21447539	C₂	1	2	yes	maximal, complemented
3	#21445865	C₂	1	1	yes	maximal, characteristic
4	#21443920	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3059	C₂	1	1	yes	maximal, characteristic
6	#16840179	—	2	4	no	—
7	C₂×#14519717	—	2	2	no	—
8	C₂×#14519717	C₂²	1	2	yes	—
9	#16839800	C₂²	1	2	yes	—
10	#16839736	—	2	1	no	—
11	#16839566	—	2	4	no	—
12	#16839519	—	2	1	no	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#536	—	2	1	no	—
16	C₆₁×#470	C₄	1	4	yes	complemented
17	C₆₁×#467	—	2	2	no	—
18	C₆₁×#427	C₂²	1	1	yes	characteristic
19	C₆₁×#419	—	2	1	no	—
20	#14519736	—	2	2	no	—
21	#14519717	—	2	4	no	—
22	#14519717	—	2	2	no	—
23	#14519717	—	2	2	no	—
24	C₂×#11758185	—	2	4	no	—
25	C₂×#11758185	D₄	1	4	yes	—
26	#14519711	—	2	2	no	—
27	#14519709	—	2	2	no	—
28	#14519692	—	4	2	no	—
29	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
30	C₂²×Q₈×C₆₁	—	2	1	no	—
31	C₂×Q₁₆×C₆₁	—	2	2	no	—
32	C₂×Q₁₆×C₆₁	—	2	1	no	—
33	C₂×Q₁₆×C₆₁	—	2	2	no	—
34	C₂×Q₁₆×C₆₁	C₂×C₄	1	2	yes	—
35	#131×C₆₁	—	2	2	no	—
36	#131×C₆₁	—	2	2	no	—
37	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₆₁	D₄	1	2	yes	—
40	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
41	C₄⋊Q₈×C₆₁	—	4	1	no	—
42	#124×C₆₁	—	4	1	no	—
43	#123×C₆₁	—	4	2	no	—
44	C₂²⋊Q₈×C₆₁	—	2	4	no	—
45	#117×C₆₁	—	2	1	no	—
46	#107×C₆₁	—	2	1	no	—
47	#106×C₆₁	C₂×C₄	1	2	yes	—
48	#103×C₆₁	—	2	4	no	—
49	#41×C₆₁	—	2	2	no	—
50	#41×C₆₁	—	2	2	no	—
51	C₂×Q₈×C₆₁	—	2	2	no	—
52	C₂×Q₈×C₆₁	—	4	1	no	—
53	C₂×Q₈×C₆₁	—	4	2	no	—
54	C₂×Q₈×C₆₁	—	4	2	no	—
55	C₂×Q₈×C₆₁	SD₁₆	1	1	yes	characteristic
56	C₂×D₄×C₆₁	D₈	1	2	yes	—
57	C₂×D₄×C₆₁	SD₁₆	1	1	yes	characteristic
58	C₂²×C₄×C₆₁	—	4	1	no	—
59	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₆₁	—	2	4	no	—
62	Q₁₆×C₆₁	—	4	1	no	—
63	Q₁₆×C₆₁	—	4	1	no	—
64	M₁₆×C₆₁	—	2	2	no	—
65	M₁₆×C₆₁	—	2	4	no	—
66	C₂×C₈×C₆₁	—	2	2	no	—
67	C₂×C₈×C₆₁	—	2	2	no	—
68	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
69	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
71	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₆₁	#41	1	2	yes	—
73	C₄⋊C₄×C₆₁	—	2	2	no	—
74	C₄⋊C₄×C₆₁	—	4	4	no	—
75	C₂²⋊C₄×C₆₁	—	4	4	no	—
76	C₂²⋊C₄×C₆₁	—	4	1	no	—
77	C₄²×C₆₁	—	4	1	no	—
78	C₂²⋊Dic₆₁	—	4	2	no	—
79	C₄⋊Dic₆₁	—	4	2	no	—
80	C₄×Dic₆₁	—	4	2	no	—
81	#11758185	—	2	4	no	—
82	C₂³×C₆₁	#102	1	2	yes	—
83	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
84	Q₈×C₆₁	—	2	2	no	—
85	Q₈×C₆₁	—	4	2	no	—
86	Q₈×C₆₁	—	4	2	no	—
87	Q₈×C₆₁	—	8	2	no	—
88	D₄×C₆₁	—	2	4	no	—
89	D₄×C₆₁	—	2	2	no	—
90	C₂×C₄×C₆₁	—	2	2	no	—
91	C₂×C₄×C₆₁	—	2	2	no	—
92	C₂×C₄×C₆₁	—	4	2	no	—
93	C₂×C₄×C₆₁	—	4	2	no	—
94	C₂×C₄×C₆₁	—	8	2	no	—
95	C₂×C₄×C₆₁	#102	1	2	yes	—
96	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₆₁	#121	1	2	yes	—
98	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
99	C₂×C₄×C₆₁	#135	1	2	yes	—
100	C₂×Dic₆₁	—	8	2	no	—
101	C₈×C₆₁	—	2	2	no	—
102	C₈×C₆₁	C₄×D₄	1	2	yes	—
103	C₈×C₆₁	#120	1	1	yes	characteristic
104	C₈×C₆₁	#123	1	1	yes	characteristic
105	#13075	—	61	1	no	maximal, Sylow
106	C₂²×C₆₁	—	2	2	no	—
107	C₂²×C₆₁	—	4	1	no	—
108	C₂²×C₆₁	—	4	2	no	—
109	C₂²×C₆₁	C₂×#102	1	1	yes	characteristic
110	C₂²×C₆₁	#466	1	2	yes	—
111	C₄×C₆₁	—	2	2	no	—
112	C₄×C₆₁	—	8	2	no	—
113	C₄×C₆₁	—	8	2	no	—
114	C₄×C₆₁	#386	1	1	yes	characteristic
115	C₄×C₆₁	#416	1	1	yes	characteristic
116	C₄×C₆₁	#465	1	2	yes	—
117	Dic₆₁	—	16	2	no	—
118	#3407	—	61	1	no	—
119	#3059	D₆₁	1	1	yes	characteristic
120	#2141	—	61	2	no	—
121	#1812	—	61	1	no	—
122	#1384	—	61	2	no	—
123	C₂×C₆₁	—	2	2	no	—
124	C₂×C₆₁	—	2	1	no	—
125	C₂×C₆₁	—	4	2	no	—
126	C₂×C₆₁	#1893	1	1	yes	characteristic
127	C₂²×Q₁₆	C₂×D₆₁	1	1	yes	characteristic
128	C₂×#131	C₂×D₆₁	1	1	yes	characteristic
129	#536	—	2	1	no	—
130	#504	—	122	4	no	—
131	C₂×M₃₂	—	61	2	no	—
132	C₂×M₃₂	—	122	2	no	—
133	#470	Dic₆₁	1	4	yes	complemented
134	#467	—	2	2	no	—
135	#427	—	61	2	no	—
136	#427	C₂×D₆₁	1	1	yes	characteristic
137	#419	—	2	1	no	—
138	#410	—	122	1	no	—
139	#358	—	122	4	no	—
140	H(3,ℤ/4)	—	122	1	no	—
141	C₆₁	#13075	1	1	yes	characteristic, complemented, Sylow
142	C₂×#41	C₂²⋊D₆₁	1	1	yes	characteristic
143	C₂²×Q₈	—	2	1	no	—
144	C₂×Q₁₆	—	2	2	no	—
145	C₂×Q₁₆	—	2	2	no	—
146	C₂×Q₁₆	—	2	1	no	—
147	C₂×Q₁₆	C₂×Dic₆₁	1	2	yes	—
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	C₂×M₁₆	C₂×Dic₆₁	1	2	yes	—
151	C₂×M₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
152	C₂²×C₈	C₂²⋊D₆₁	1	2	yes	—
153	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
154	C₄⋊Q₈	—	4	1	no	—
155	#124	—	4	1	no	—
156	#123	—	4	2	no	—
157	C₂²⋊Q₈	—	2	4	no	—
158	#117	—	2	1	no	—
159	#117	—	122	2	no	—
160	M₃₂	—	122	4	no	—
161	M₃₂	—	122	2	no	—
162	M₃₂	—	122	2	no	—
163	C₂×C₁₆	—	61	4	no	—
164	C₂×C₁₆	—	122	4	no	—
165	#107	—	2	1	no	—
166	#107	—	122	2	no	—
167	#106	—	122	2	no	—
168	#106	C₂×Dic₆₁	1	2	yes	—
169	#103	—	2	4	no	—
170	#99	—	244	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	#11758200	1	1	yes	characteristic
178	C₂×D₄	#11758199	1	2	yes	—
179	C₂×D₄	#11758200	1	1	yes	characteristic
180	C₂²×C₄	—	4	1	no	—
181	C₂²×C₄	C₂²⋊Dic₆₁	1	2	yes	—
182	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
183	Q₁₆	—	2	4	no	—
184	Q₁₆	—	4	1	no	—
185	Q₁₆	—	4	1	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	4	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	C₂²⋊Dic₆₁	1	2	yes	—
191	C₂×C₈	D₄×D₆₁	1	2	yes	—
192	C₂×C₈	#11758224	1	2	yes	—
193	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
194	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	4	4	no	—
197	C₄⋊C₄	—	244	2	no	—
198	C₂²⋊C₄	—	4	4	no	—
199	C₂²⋊C₄	—	4	1	no	—
200	C₂²⋊C₄	—	244	2	no	—
201	C₄²	—	4	1	no	—
202	C₄²	—	244	2	no	—
203	C₁₆	—	122	4	no	—
204	C₂³	#14519698	1	2	yes	—
205	C₂³	C₂×#11758199	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	4	2	no	—
209	Q₈	—	8	2	no	—
210	D₄	—	2	4	no	—
211	D₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	488	2	no	—
218	C₂×C₄	#14519698	1	2	yes	—
219	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
220	C₂×C₄	#14519749	1	2	yes	—
221	C₂×C₄	C₂×#11758200	1	1	yes	characteristic
222	C₂×C₄	#14519797	1	2	yes	—
223	C₈	—	2	2	no	—
224	C₈	D₄×Dic₆₁	1	2	yes	—
225	C₈	#14519745	1	1	yes	characteristic
226	C₈	#14519758	1	1	yes	characteristic
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂×#14519698	1	1	yes	characteristic
231	C₂²	#16839996	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	8	2	no	—
234	C₄	—	8	2	no	—
235	C₄	—	976	2	no	—
236	C₄	#16839642	1	1	yes	characteristic
237	C₄	#16839758	1	1	yes	characteristic
238	C₄	#16839989	1	2	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#21446248	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21458922

C₂

yes

maximal, characteristic

#21447539

C₂

yes

maximal, complemented

#21445865

C₂

yes

maximal, characteristic

#21443920

C₂

yes

maximal, complemented

C₆₁×#3059

C₂

yes

maximal, characteristic

#16840179

—

C₂×#14519717

—

C₂×#14519717

C₂²

yes

—

#16839800

C₂²

yes

—

#16839736

—

#16839566

—

#16839519

—

C₂²×Q₁₆×C₆₁

C₂²

yes

characteristic

C₂×#131×C₆₁

C₂²

yes

characteristic

C₆₁×#536

—

C₆₁×#470

C₄

yes

complemented

C₆₁×#467

—

C₆₁×#427

C₂²

yes

characteristic

C₆₁×#419

—

—

—

—

—

—

D₄

yes

—

#14519711

—

#14519709

—

#14519692

—

C₂×#41×C₆₁

D₄

yes

characteristic

C₂²×Q₈×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

C₂×C₄

yes

—

#131×C₆₁

—

#131×C₆₁

—

C₂×M₁₆×C₆₁

C₂×C₄

yes

—

C₂×M₁₆×C₆₁

D₄

yes

characteristic

C₂²×C₈×C₆₁

D₄

yes

—

C₂²×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊Q₈×C₆₁

—

#124×C₆₁

—

#123×C₆₁

—

C₂²⋊Q₈×C₆₁

—

#117×C₆₁

—

#107×C₆₁

—

#106×C₆₁

C₂×C₄

yes

—

#103×C₆₁

—

#41×C₆₁

—

#41×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

SD₁₆

yes

characteristic

C₂×D₄×C₆₁

D₈

yes

—

C₂×D₄×C₆₁

SD₁₆

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

Q₁₆×C₆₁

—

Q₁₆×C₆₁

—

Q₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂²⋊C₄

yes

—

C₂×C₈×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×D₄

yes

—

C₂×C₈×C₆₁

C₂×D₄

yes

characteristic

C₂×C₈×C₆₁

#41

yes

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

#11758185

—

C₂³×C₆₁

#102

yes

—

C₂³×C₆₁

C₂×D₈

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

#102

yes

—

C₂×C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

#121

yes

—

C₂×C₄×C₆₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₆₁

#135

yes

—

100

C₂×Dic₆₁

—

101

C₈×C₆₁

—

102

C₈×C₆₁

C₄×D₄

yes

—

103

C₈×C₆₁

#120

yes

characteristic

104

C₈×C₆₁

yes

105

—

106

C₂²×C₆₁

—

107

C₂²×C₆₁

—

108

C₂²×C₆₁

—

109

C₂²×C₆₁

C₂×#102

yes

characteristic

110

C₂²×C₆₁

#466

yes

—

111

C₄×C₆₁

—

112

C₄×C₆₁

—

113

C₄×C₆₁

—

114

C₄×C₆₁

#386

yes

characteristic

115

C₄×C₆₁

#416

yes

characteristic

116

C₄×C₆₁

#465

yes

—

117

Dic₆₁

—

118

#3407

—

119

#3059

D₆₁

yes

characteristic

120

#2141

—

121

#1812

—

122

#1384

—

123

C₂×C₆₁

—

124

C₂×C₆₁

—

125

C₂×C₆₁

—

126

C₂×C₆₁

#1893

yes

characteristic

127

C₂²×Q₁₆

C₂×D₆₁

yes

characteristic

128

C₂×#131

C₂×D₆₁

yes

characteristic

129

#536

—

130

#504

—

122

—

131

C₂×M₃₂

—

132

C₂×M₃₂

—

122

—

133

#470

Dic₆₁

yes

complemented

134

#467

—

135

#427

—

136

#427

C₂×D₆₁

yes

characteristic

137

#419

—

138

#410

—

122

—

139

#358

—

122

—

140

H(3,ℤ/4)

—

122

—

141

C₆₁

#13075

yes

characteristic, complemented, Sylow

142

C₂×#41

C₂²⋊D₆₁

yes

characteristic

143

C₂²×Q₈

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

C₂×Dic₆₁

yes

—

148

#131

—

149

#131

—

150

C₂×M₁₆

C₂×Dic₆₁

yes

—

151

C₂×M₁₆

C₂²⋊D₆₁

yes

characteristic

152

C₂²×C₈

C₂²⋊D₆₁

yes

—

153

C₂²×C₈

C₂²×D₆₁

yes

characteristic

154

C₄⋊Q₈

—

155

#124

—

156

#123

—

157

C₂²⋊Q₈

—

158

#117

—

159

#117

—

122

—

160

M₃₂

—

122

—

161

M₃₂

—

122

—

162

M₃₂

—

122

—

163

C₂×C₁₆

—

164

C₂×C₁₆

—

122

—

165

#107

—

166

#107

—

122

—

167

#106

—

122

—

168

#106

C₂×Dic₆₁

yes

—

169

#103

—

170

#99

—

244

—

171

#41

—

172

#41

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

#11758200

yes

characteristic

178

C₂×D₄

#11758199

yes

—

179

C₂×D₄

#11758200

yes

characteristic

180

C₂²×C₄

—

181

C₂²×C₄

C₂²⋊Dic₆₁

yes

—

182

C₂²×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

183

Q₁₆

—

184

Q₁₆

—

185

Q₁₆

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

C₂²⋊Dic₆₁

yes

—

191

C₂×C₈

D₄×D₆₁

yes

—

192

C₂×C₈

#11758224

yes

—

193

C₂×C₈

C₂²×Dic₆₁

yes

characteristic

194

C₂×C₈

C₂×C₂²⋊D₆₁

yes

characteristic

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

244

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

244

—

201

C₄²

—

202

C₄²

—

244

—

203

C₁₆

—

122

—

204

C₂³

#14519698

yes

—

205

C₂³

C₂×#11758199

yes

characteristic

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

Q₈

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

488

—

218

C₂×C₄

#14519698

yes

—

219

C₂×C₄

C₂×C₂²⋊Dic₆₁

yes

characteristic

220

C₂×C₄

#14519749

yes

—

221

C₂×C₄

C₂×#11758200

yes

characteristic

222

C₂×C₄

#14519797

yes

—

223

C₈

—

224

C₈

D₄×Dic₆₁

yes

—

225

C₈

#14519745

yes

characteristic

226

C₈

#14519758

yes

characteristic

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂×#14519698

yes

characteristic

231

C₂²

#16839996

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

976

—

236

C₄

#16839642

yes

characteristic

237

C₄

#16839758

yes

characteristic

238

C₄

#16839989

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#21446248

yes

characteristic

	subgroup	G/H
center	C₂	#21446248
commutator	C₂×C₈×C₆₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₁
Fitting	C₆₁×#3059	C₂
socle	C₂×C₆₁	#1893
prime radical	C₂×#41×C₆₁	D₄
cosocle	C₂²×C₈×C₆₁	C₂³
hypercenter	#3059	D₆₁
hypocenter	C₆₁	#13075
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

subgroup

G/H

center

C₂

#21446248

commutator

C₂×C₈×C₆₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₁

Fitting

C₆₁×#3059

C₂

socle

C₂×C₆₁

#1893

prime radical

C₂×#41×C₆₁

D₄

cosocle

C₂²×C₈×C₆₁

C₂³

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

N	H ≅ G/N	type
2. #21447539	C₂	semidirect
4. #21443920	C₂	semidirect
16. C₆₁×#470	C₄	semidirect
133. #470	Dic₆₁	semidirect
141. C₆₁	#13075	semidirect

H ≅ G/N

type

2. #21447539

C₂

semidirect

4. #21443920

C₂

semidirect

16. C₆₁×#470

C₄

semidirect

133. #470

Dic₆₁

semidirect

141. C₆₁

#13075

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21458922	2
#21447539	2
#21445865	2
#21443920	2
C₆₁×#3059	2
#13075	61

subgroup

index

C₆₁×#3059

Subgroups — #29597468

Conjugacy classes of subgroups

Complements

Maximal subgroups